CN1857796B - Rotor mechanical device - Google Patents

Abstract

The rotor machine has unchanged operating space. Technologically, the rotor machine is provided with two, one right and one left, pistons inside guide drum fixed on the machine, and two, one right and one left, rotor contacting separately to the right and the left pistons. One right contact part and one contact part are set between the each piston and each rotor for tangent contact, so as to maintain the operating space of the machine unchanged, eliminate the ellipticity error caused by rotor inclination and geometric error caused by point contact, and ensure strict simple harmonic vibration.

Description

A kind of rotor mechanical device

Technical field

The present invention relates to a kind ofly produce reciprocating mechanical device, belong to theory of mechanics, theory of mechanisms technical field by rotor.

Background technology

Produce oscillating movement, can utilize eccentric rotor.As a kind of mechanical device, eccentric rotor can be used in many machinery equipments.No matter but be prior art or theory, do not notice that all eccentric rotor in fact only guarantees that its center of circle does simple harmonic oscillation, can not guarantee under some situation to make same simple harmonic oscillation and the relevant issues that cause thus, thereby can not keep the constant pressure that influences medium in the equipment, can not eliminate ovality influence that rotor causes because of inclination etc. as the distance between the two-piston inner face that drives by rotor by the member (as piston) that rotor drives; In addition, general disc-like rotor can not change the amplitude of vibration.The invention provides a kind of improved rotor mechanism, be characterized in: 1. rotor more than cooperates.2. parameters such as geometry that can be by changing rotor, size, position, rotating speed make the member (as piston) that is driven by rotor obtain the required characteristics of motion.3. the member that is driven by rotor is done with rotor same frequency (cycle), with the simple harmonic oscillation of amplitude, and made the distance between the two-piston inner face that drives by rotor keep constant, thereby eliminate influence pressure medium in the equipment.4. the speed of rotor (cycle), amplitude can be regulated accurately and easily.The present invention and the stroke of rotor mechanism is provided and the calculating of speed etc. with figure.

Summary of the invention

The purpose of this invention is to provide a kind of rotor mechanical device, particularly a kind of improved rotor mechanical device.

The technical solution adopted for the present invention to solve the technical problems is: use a kind of improved rotor mechanical device, it comprises piston 10, piston waveguide tube 4, equipment 6 and rotor 3,4 one-tenth sealings of piston 10 and piston waveguide tube can be movingly, and rotor 3 driven plunger 10 are moved in piston waveguide tube 4.Desire to make piston 10 to obtain simple harmonic oscillation, and the locus of equipment 6 between two-piston 10 inner faces changed by the simple harmonic oscillation rule, and the space size remains unchanged, can the contact 12 vertical with its center line be set in piston 10 outer ends, contact 12 is contacted with the cross section tangentially of rotor 3.

Described rotor 3 comprises disc-like rotor or column rotor, and rotor 3 is fixed or removable in its rotating shaft 2 directions, and the geometrical axis of rotor 3 intersects or intersects with its rotating shaft 2 or be parallel or overlap.Described disc-like rotor 3 comprises circular section rotor or on-circular cross-section rotor, and described column rotor 3 comprises cylinder, round platform or on-circular cross-section cylinder.To on-circular cross-section rotor 3, the variable in distance between the stroke of piston 10, speed and two-piston 10 inner faces can determine by the concrete cross sectional shape of design rotor 3.The geometrical axis of described piston 10 intersects or intersects with the geometrical axis or the rotating shaft 2 of rotor 3.The shape of described equipment 6 comprises curve-like or linearity, and mounting means is vertical horizontal or tilting.

The invention has the beneficial effects as follows: under on-circular cross-section rotor 3 situations, intracavity space length and the stroke of position and piston 10 and the speed of equipment 6 between two-piston 10 inner faces can be according to parameters such as the shape of rotor 3, size, orientation and change; Under circular section rotor 3 situations, 1) if the outer end of piston 10 contacts with 3 of rotors, intracavity space length and the stroke of position and piston 10 and the speed of equipment 6 between two-piston 10 inner faces can be determined by computing formula or the figure that this specification provides, 2) if the contact 12 vertical with its center line is set in the outer end of piston 10, piston 10 is done and the same simple harmonic oscillation in rotor 3 centers of circle, eliminate the ovality influence that rotor 3 causes because of inclination or eliminate length variations between two-piston 10 inner faces, keep the length between two-piston 10 inner faces invariable in two-piston 10 runnings, thereby eliminate influence pressure medium in the equipment 6; The rotating speed that changes rotor 3 power set (as motor) just can change the speed of rotor 3, and is removable in its rotating shaft 2 directions because of rotor 3 again, and the position that changes rotor 3 can change its amplitude.

Description of drawings

Fig. 1 is the some contact cylindrical rotor mechanism of installing with axial symmetry.

Fig. 2 is that explanation rotor 3 geometric center a points are the figure of simple harmonic motion at the stroke of vertical.

Fig. 3 is near the left and right rotor 3 local figure the piston 10.

To be left rotor 3 rotate to and make it be in the front view of extreme lower position from making piston 10 be in the extreme higher position Fig. 4.

To be left rotor 3 rotate to and make it be in the cross-sectional view of extreme lower position from making piston be in the extreme higher position Fig. 5.

Fig. 6 is that the son 3 of turning right rotates to and makes it be in the cross-sectional view of extreme higher position from making piston be in extreme lower position.

Fig. 7 is the comparison of λ=0.1 o'clock any time addition Item and simple harmonic quantity item.

Fig. 8 is the comparison of λ=0.5 o'clock any time addition Item and simple harmonic quantity item.

Fig. 9 is the stroke of left piston 10 under the different λ of any time.

Figure 10 is the speed of left piston 10 under the different λ of any time.

Figure 11 is the variable in distance between two-piston 10 inner faces under the different λ of any time.

Figure 12 is that turn right height that son 3 rotates to β place piston 10 and left rotor 3 of explanation rotates to the figure that the height of 180 °-β place piston 10 equates.

Figure 13 is that the stroke ratio of λ=0.1 left and right piston 10 of some any time reaches the spacing variation.

Figure 14 is that the stroke ratio of λ=0.5 left and right piston 10 of some any time reaches the spacing variation.

Figure 15 is that the stroke ratio of λ=0.8 left and right piston 10 of some any time reaches the spacing variation.

Figure 16 is the λ=0.1 o'clock speed contrast of instantaneous left and right piston 10 arbitrarily.

Figure 17 is the λ=0.5 o'clock speed contrast of instantaneous left and right piston 10 arbitrarily.

Figure 18 is the λ=0.8 o'clock speed contrast of instantaneous left and right piston 10 arbitrarily.

Figure 19 is the oval cross section of rotor 3 in vertical.

Figure 20 is the analysis chart that left rotor 3 is considered ovality.

Figure 21 is the analysis chart that right-hand rotation 3 is considered ovalitys.

Figure 22 is α=30 °, the λ=0.5 o'clock ovality figure that influences to stroke, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 23 is α=30 °, the λ=0.8 o'clock ovality figure that influences to stroke, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 24 is α=15 °, the λ=0.5 o'clock ovality figure that influences to stroke, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 25 is α=15 °, the λ=0.3 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 26 is α=30 °, the λ=0.3 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 27 is α=15 °, the λ=0.5 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 28 is α=30 °, the λ=0.5 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 29 is α=15 °, the λ=0.8 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 30 is α=30 °, the λ=0.8 o'clock ovality figure that influences to length variations δ between two-piston 10 inner faces, and wherein the situation of ovality is disregarded in 1 representative, and the situation of ovalitys is considered in 2 representatives.

Figure 31 is α=30 °, the λ=0.1 o'clock ovality figure that influences to piston 10 speed.

Figure 32 is α=15 °, the λ=0.3 o'clock ovality figure that influences to piston 10 speed.

Figure 33 is α=30 °, the λ=0.3 o'clock ovality figure that influences to piston 10 speed, the speed of left rotor when wherein ovality is disregarded in 1 representative, the speed of right-hand rotation when ovality is disregarded in 1 ' representative, the speed of left rotor when ovality is considered in 2 representatives, the speed of the son of turning right when ovality is considered in 2 ' representative.

Figure 34 is α=15 °, the λ=0.5 o'clock ovality figure that influences to piston 10 speed.

Figure 35 is α=30 °, the λ=0.5 o'clock ovality figure that influences to piston 10 speed, the speed of left rotor when wherein ovality is disregarded in 1 representative, the speed of right-hand rotation when ovality is disregarded in 1 ' representative, the speed of left rotor when ovality is considered in 2 representatives, the speed of the son of turning right when ovality is considered in 2 ' representative.

Figure 36 is α=15 °, the λ=0.8 o'clock ovality figure that influences to piston 10 speed.

Figure 37 is α=30 °, the λ=0.8 o'clock ovality figure that influences to piston 10 speed, the speed of left rotor when wherein ovality is disregarded in 1 representative, the speed of right-hand rotation when ovality is disregarded in 1 ' representative, the speed of left rotor when ovality is considered in 2 representatives, the speed of the son of turning right when ovality is considered in 2 ' representative.

Left and right rotor 3 local figure when Figure 38 is the tangent line contact.

To be tangent line when contact left rotor 3 rotate to and make it be in the figure of extreme lower position from making piston 10 be in the extreme higher position Figure 39.

Figure 40 is that the son 3 of turning right in tangent line when contact rotates to and makes it be in the figure of extreme higher position from making piston be in extreme lower position.

Figure 41 is a rotor 3 when contacting with piston 10 outer end points, and the motion of left and right piston 10 is the analyzing chart for reason of symmetry not exclusively.

Figure 42 further specifies the difference plot (dotted line is a tangent line contact situation) that a contact contacts with tangent line.

Figure 43 is a cam follower 3.

Figure 44 is an odd-shaped cross section rotor 3.

Figure 45 is a plate-like eccentric rotor 3.

Figure 46 is that round platform is just being put rotor 3.

Figure 47 is a round platform biasing rotor 3.

Among the figure: 1, bearing, 2, rotating shaft, 3, rotor, 4, piston waveguide tube, 5, pad, 6, equipment, 7, bolt and nut component, 8, sealing ring, 9, spring, 10, piston, 11, the contact ball, 12, contact.

The specific embodiment

Embodiment 1, curved equipment 6 is sealedly and fixedly connected for 4 one-tenth with piston waveguide tube by flange, bolt, gasket assembly, equipment 6 can vertical installation also can horizontally be installed (this example is vertical installation), piston 10 can be movingly by 4 one-tenth sealings of potted component and piston waveguide tube, and 3 one-tenth points of piston 10 outer ends (can be piston rod in case of necessity) and rotor contact.Drive cylindrical rotor 3 by power set (as motor), because rotor 3 geometrical axis and its rotation 2 have an angle α, thereby there is eccentric throw in rotor 3, and the rotation of rotor 3 just promotes piston 10 and pumps, make the intracavity space of equipment 6, thereby make the medium in the equipment 6 produce vibration.This example contacts for 3 one-tenth points of piston 10 outer ends (can be piston rod in case of necessity) and rotor, and (surplus) string rule so the motion of piston 10 just is being as the criterion is specifically seen relevant formula of following " motion analysis " part and the relevant drawings in " Figure of description ".Rotor 3 can move changing eccentric throw along its axis direction, thereby changes the parameters such as distance of 10 of the amplitude of piston 10 and two-pistons.The rotating speed of rotor 3 can change by the rotating speed of regulating drive unit, thereby changes the vibration frequency of piston 10.Consult Fig. 1.

Embodiment 2, if will overcome the ovality influence of tilting to be caused because of rotor 3, keep the big or small constant of equipment 6 intracavity spaces (being the distance between two-piston 10 inner faces), and piston 10 is done and the identical simple harmonic oscillation in rotor 3 centers of circle, can piston 10 outer ends (can be piston rod in case of necessity) add one with the vertical contact 12 of piston 10 center lines (or rotor 3 axis or rotating shaft 2), contacted with rotor 3 tangentiallies by contact 12, all the other are with embodiment 1.Consult Fig. 1, Figure 38, Figure 39 and Figure 40.

Embodiment 3, change the circular section rotor 3 among the embodiment 1 into cam follower 3, and all the other are with embodiment 1.Consult Fig. 1, Figure 43.When piston 10 contacted with cam follower 3, the forms of motion of several pistons 10 commonly used had:

1) movement at the uniform velocity

Rise: Backhaul:

2) etc. quicken uniform retarded motion

Rise acceleration such as () being made as: Backhaul decelerations such as () being made as:

3) sinusoidal accelerated motion

$\frac{a}{{\mathrm{\δ}}_0}\left(\frac{2\mathrm{\π}}{{\mathrm{\δ}}_0}\mathrm{\δ}\right)$

4) cosine accelerated motion

$u=\frac{\mathrm{\πa}}{2{\mathrm{\δ}}_0}\left(\frac{\mathrm{\π}}{{\mathrm{\δ}}_0}\mathrm{\δ}\right)$

Embodiment 4, change the circular section rotor 3 among the embodiment 1 into odd-shaped cross section rotor 3, and all the other are with embodiment 1.Consult Fig. 1, Figure 44.When piston 10 contacts with odd-shaped cross section rotor 3, can obtain the characteristics of motion relevant, and the cross sectional shape of rotor 3 can design as required with the cross sectional shape of rotor 3.

Embodiment 5, if only need overcome because the ovality influence that rotor 3 tilts to be caused can change the column among the embodiment 1 (circular section) rotor 3 into plate-like eccentric rotor 3, all the other are with embodiment 1.Consult Fig. 1, Figure 45.The geometrical axis of this routine rotor 3 is parallel with its rotating shaft 2, and cross section does not have ovality for circle.

Carry out motion analysis below in conjunction with accompanying drawing.Figure 1 shows that piston and equipment (being vertical installation) that symmetry is installed in the cylindrical rotor in the same rotating shaft and is promoted by rotor here.Rotor shaft and its geometric center lines have an angle α, make the intersection point o that is not in rotating shaft and rotor geometric center lines when piston " above the time, rotor has an eccentric distance e, thereby can promote piston reciprocates and finish certain production process.Rotor can also move along its rotating shaft direction, so that change the size of eccentric throw, promptly changes the amplitude of piston.The rotor symmetry is installed, be that the level inclination of left and right rotor is identical but direction is opposite, in the piston running, the extreme higher position of its inner face is+e, promptly, the high energy of left piston inner face reaches the m-m cross section of Fig. 1, and the high energy of right piston inner face reaches m '-m ' cross section of Fig. 1, and m-m and m '-m ' cross section is at sustained height; The extreme lower position of piston inner face is-e, that is, the low energy of left piston inner face reaches the n-n cross section of Fig. 1, and the low energy of right piston inner face reaches n '-n ' cross section of Fig. 1, and n-n and n '-n ' cross section is at sustained height; Therefore the total kilometres of piston distance is 2e, and amplitude is e; The stroke distances of piston is 0 during the equilbrium position, sees o-o cross section and the o '-o ' cross section of Fig. 1, and o-o and o '-o ' cross section is at sustained height.Obviously, when rotor rotates with angular velocity omega, the rotor geometric cross-section center a at piston place is ecos β at the stroke of vertical, wherein β is the rotor geometric cross-section center a at rotor place, piston place when rotating to the optional position and the line of pivot b (wire length is for being eccentric distance e) and the angle of vertical, β=ω t, t is the time, sees Fig. 2, L represents left rotor among the figure, and the R representative is turned right sub (down together).Following motion analysis can prove simultaneously, structure for Fig. 1, though the rotor symmetry is installed, but under piston outer end and situation that rotor point contacts, a left side, the reciprocating motion of right piston is not strict symmetry, that is: the distance of left piston inner face rising is not to equal the distance that right piston inner face descends constantly, that is: a left side, right piston inner face at any time or the stroke at any position angle β place not be to be simple harmonic oscillation rule ecos β and-ecos β (or-ecos β and ecos β), but the distance that a left side (right side) piston rises is slightly less than the distance that the right side (left side) piston descends, thereby the length between the two-piston inner face is slightly increased.Eliminate this kind phenomenon and guarantee left and right piston inner face at any time or the stroke at any position angle β place be simple harmonic oscillation rule ecos β and-ecos β (or-ecos β and ecos β), thereby it is constant to keep equipment intracavity space size, only need the line way of contact is changed in the some way of contact of piston outer end and rotor, promptly add a contact and get final product, or change the rotor shapes and/or the characteristics of motion in the piston outer end.For analyzing the motion of rotor mechanism, get near the part rotor of piston and be plotted in Fig. 3.

1, the piston outer end contacts with rotor point

Fig. 3 promptly is the situation that the piston outer end contacts with rotor point.If initial moment left piston is in the extreme higher position, right piston is in the extreme higher position.Fig. 4 rotates to and makes piston be in the front view of extreme lower position from making piston be in the extreme higher position for left rotor, Fig. 5 rotates to and makes cross-sectional view that piston is in extreme lower position (among Fig. 1 from right to left from making piston be in the extreme higher position for left rotor, down with), Fig. 6 rotates to and makes piston be in the cross-sectional view of extreme higher position from making piston be in extreme lower position for the son of turning right.

The motion of left rotor is discussed earlier.Consult Fig. 5, when rotor rotates to any position angle β, have according to geometrical relationship:

$\mathrm{ki}=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}$

kb＝ecosβ

Contact point i is to the distance of centre of gyration b

${\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2006100843262E00011.png,H2006100843262E00033.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=\mathrm{ib}=\mathrm{ki}+\mathrm{kb}=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}+e\cos \mathrm{\&beta;}$

I is the stroke of piston inner face to the distance of 0-0:

${\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2006100843262E00011.png,H2006100843262E00033.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=z_1-R=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}+e\cos \mathrm{\&beta;}-R---\left(1\right)$

As seen, the left piston inner face is carved at a time or the stroke at certain position angle β place is not ecos β, but as the formula (1).Wherein

Being addition Item, is the simple harmonic oscillation stroke with e and the equal relevant ecos β of R, only relevant with e, irrelevant with R.

For ease of analyzing order

$\frac{z}{e}=\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1/\mathrm{\&lambda;}+\cos \mathrm{\&beta;}---\left(2\right)$

More than various in

E-eccentricity of rotor R-rotor radius ω-rotor velocity

β (=ω t)-rotor position angle λ-λ=e/R

Any time, i.e. angle, optional position β place addition Item

With simple harmonic oscillation item ξ=cos β and ξ=-cos β (representative turn right son) relatively see Fig. 7 (λ=0.1) and Fig. 8 (λ=0.5).These figure show that the characteristics of motion of piston is taken addition Item as the leading factor with simple harmonic oscillation rule cos β

Influence to simple harmonic oscillation item cos β is relevant with the size of λ, λ hour, influence is little; When λ is big, certain influence is arranged.

Piston movement speed

$u=\frac{\mathrm{dz}}{\mathrm{dt}}=-\frac{\mathrm{e\&omega;}\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}}{\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}-\mathrm{e\&omega;}\sin \mathrm{\&beta;}---\left(3\right)$

Or $\frac{u}{u_o}=-\sin \mathrm{\&beta;}(\frac{\cos \mathrm{\&beta;}}{\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}+1)---\left(4\right)$

U wherein _o=e ω is the linear velocity of rotor cross-section geometric center a around its pivot b.Fig. 9,10 has drawn the stroke and the speed of left piston under the different λ of any time respectively.

The sub displacement of turning right is derived as follows.Referring to Fig. 6.

$\mathrm{ki}=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}},\mathrm{kb}=e\cos \mathrm{\&beta;}$

Owing to be in the extreme higher position at the initial time left rotor, right-hand rotation is in extreme lower position, so the original position of the sub-anglec of rotation β that turns right as shown in Figure 6.Contact point i is to the distance of centre of gyration b

${\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">z</figure-callout>}}_2=\mathrm{ib}=\mathrm{ki}-\mathrm{kb}=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-e\cos \mathrm{\&beta;}$

Contact point is to the distance of 0-0

$z^{\&prime;}=\sqrt{R^2-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">e</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-R-e\cos \mathrm{\&beta;}---\left(5\right)$

$\frac{z^{\&prime;}}{e}=\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1/\mathrm{\&lambda;}-\cos \mathrm{\&beta;}---\left(6\right)$

The distance that the right as can be known piston of contact formula (1) rises or descends also is not equal to the distance that left piston descends or rises.

Does the two gap have much? make left and right piston stroke sum

$\mathrm{\&Delta;}=z+z^{\&prime;}=2R(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)---\left(7\right)$

If the distance that right piston rises or descends equals the distance that left piston descends or rises, then Δ should be 0, so Δ in fact also is the variable in distance between the two-piston inner face under the different λ of arbitrary moment.Obviously Δ is impermanent is 0, and this represents when rotor contacts with piston point, because left and right rotor is not separately with the operation of simple harmonic oscillation rule, so displacement of the two and incomplete symmetry.Know by formula (7), Δ＜0, this expression is to structure shown in Figure 1, distance in mechanism's running between the two-piston inner face slightly is enlarging state all the time, the pressure that can not cause medium in the equipment increases, and is applicable to that the device space needs the occasion of slightly increase or the little occasion of the influence of increase slightly in space; The occasion that the pressure that does not allow in the equipment is reduced has certain influence.The distance between the two-piston inner face is deflated state in the running if will make, and only need correspondingly change the geometry in rotor cross section.Formula (7) shows that also Δ is a symmetry with 90 °, and ° locates to be maximum (negative) in β=90, is the cycle with 180 °.Order

$\mathrm{\&delta;}=\mathrm{\&Delta;}/e=\frac{z}{e}+\frac{z^{\&prime;}}{e}=\frac{2}{\mathrm{\&lambda;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)---\left(8\right)$

Under some λ the δ at arbitrary moment β place as shown in figure 11, δ also is the influence that is subjected to λ, λ is big more, δ is big more.Change the size of δ, only need to regulate λ and get final product.With R=80mm is example, establishes λ=0.5, so e=λ R=40mm, Δ=δ e=-0.5359 * 40=-21.4mm ° is located in β=90, establishes device length L=2000mm again, Δ/L=21.4/2000=1.07%.

According to sin (180 °-β)=sin β and cos (180 °-β)=-cos β, comparison expression (2) and formula (6) are as can be known This relation also can intuitively be illustrated by Figure 12.Arbitrary left and right rotor of the moment under some λ

See Figure 13,14 and 15, drawn the variation of two-piston spacing among the figure simultaneously, promptly

Although as seen piston is not with the regular movement of pure simple harmonic oscillation ecos β, but still for being the reciprocating motion in cycle with 2 π.These figure also can be used for looking into the stroke z/e that gets any time piston.

To the son of turning right, u '=dz '/dt puts this formula of formula (5) substitution in order

$\frac{u^{\&prime;}}{u_o}=\sin \mathrm{\&beta;}(1-\frac{\cos \mathrm{\&beta;}}{\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}})---\left(9\right)$

With sin (180 °+β)=-sin β, cos (180 °+β)=-cos β substitution formula (9)

$\frac{u^{\&prime;}}{u_o}=-\sin \mathrm{\&beta;}(\frac{\cos \mathrm{\&beta;}}{\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}+1)$

As seen turning right, ° speed of locating is identical in β+180 with left rotor for the speed of son at the β place.The speed of left and right rotor is seen Figure 16,17 and 18.These figure also can be used for looking into the speed u/u that gets any time piston _o

2, the influence of ovality under the some contact situation

Strictly speaking, because rotor with respect to the horizontal plane has an inclined angle alpha, rotor is at the cross section and the on-circular cross-section of vertical, but ellipsoid is seen Figure 19.The analysis chart of considering ovality is shown in Figure 20 and 21.

Referring to Figure 19,20 and 21, oval long and short semiaxis is respectively R/cos α, R, thereby its equation is

$\frac{x^2}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{y^2}{{(R/\cos \mathrm{\&alpha;})}^2}=1$ Promptly $\frac{x^2}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{y^2}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&alpha;}=1$

Formula solves thus

$\frac{\sqrt{R^2-x^2}}{\cos \mathrm{\&alpha;}}\left(10\right)$

When piston was in optional position β, x=esin β was got by formula (12)

$y=\frac{R\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}{\cos \mathrm{\&alpha;}}$

To left rotor (consulting Figure 20): z ₁=y+ecos β

And $z=z_1-R/\cos \mathrm{\&alpha;}=\frac{R}{\cos \mathrm{\&alpha;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)+e\cos \mathrm{\&beta;}$ So

$\frac{z}{e}=\frac{1}{\mathrm{\&lambda;}\cos \mathrm{\&alpha;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)+\cos \mathrm{\&beta;}---\left(11\right)$

With the piston stroke of disregarding ovality

$\frac{z}{e}=\frac{1}{\mathrm{\&lambda;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)+\cos \mathrm{\&beta;}$

Comparison, last extention just considering the stroke under the ovality situation are to disregard the 1/cos α of the addition Item of ovality situation doubly.

Know β=0 o'clock, z/e=1 by formula (11); β=180 o'clock, z/e=-1.As seen z/e is still as the situation of disregarding ovality, between-1～+ 1, promptly the stroke of piston still be-e～+ e, that is piston amplitude still is e.

To the son of turning right (consulting Figure 21): z ₂=y-ecos β

$z^{\&prime;}=z_2-R/\cos \mathrm{\&alpha;}=\frac{R}{\cos \mathrm{\&alpha;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)-e\cos \mathrm{\&beta;}$

$\frac{z^{\&prime;}}{e}=\frac{1}{\mathrm{\&lambda;}\cos \mathrm{\&alpha;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)-\cos \mathrm{\&beta;}---\left(12\right)$

As seen the stroke of right piston also be-e～+ e, piston amplitude also is e.

With disregard ovality piston stroke

$\frac{z^{\&prime;}}{e}=\frac{1}{\mathrm{\&lambda;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)-\cos \mathrm{\&beta;}$

Comparison, last extention just considering the stroke of ovality situation also are to disregard the 1/cos α of the addition Item of ovality situation doubly.Figure 22 to 24 is for considering ovality and the comparison of disregarding ovality situation bottom left rotor stroke, and the situation of ovality is disregarded in 1 expression among the figure, and the situation of ovality is considered in 2 expressions.By figure and formula (12) as seen, the difference of the two is relevant with α and λ, can adjust the difference of the two by adjusting α and λ.

Be similar to the situation of disregarding ovality, can derive that length variations is between the two-piston inner face

$\mathrm{\&delta;}=\mathrm{\&Delta;}/e=\frac{z}{e}+\frac{z^{\&prime;}}{e}=\frac{2}{\mathrm{\&lambda;}\cos \mathrm{\&alpha;}}(\sqrt{1-{\mathrm{\&lambda;}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}-1)---\left(13\right)$

Figure 25～30 are the comparison of δ under consideration ovality and the situation of disregarding ovality.From figure and formula (13) as can be known, hour the two does not almost have difference at λ and α, and along with λ and/or α increase, the two visible difference occurs.In any case but δ can not surpass 2e yet in the engineering reality, this order of magnitude is compared very little with the length between two-piston, if pressure is not strict with, then influence is little; Only certain influence is just arranged in the occasion that pressure is had strict demand.

To left rotor

$u=\frac{\mathrm{dz}}{\mathrm{dt}}=-\frac{\mathrm{e\&omega;}\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}}{\cos \mathrm{\&alpha;}\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}-\mathrm{e\&omega;}\sin \mathrm{\&beta;}---\left(14\right)$

$\frac{u}{u_o}=-\sin \mathrm{\&beta;}(\frac{\cos \mathrm{\&beta;}}{\cos \mathrm{\&alpha;}\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}+1)---\left(15\right)$

To the son of turning right

U '=dz '/dt puts this formula of formula (12) substitution in order

$\frac{u^{\&prime;}}{u_o}=\sin \mathrm{\&beta;}(1-\frac{\cos \mathrm{\&beta;}}{\cos \mathrm{\&alpha;}\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}})---\left(16\right)$

U wherein _o=e ω still is the linear velocity of rotor geometric center a around pivot b.

With sin (180 ° of β)=-sin β, cos (180 °+β)=-cos β substitution formula (16)

$\frac{u^{\&prime;}}{u_o}=-\sin \mathrm{\&beta;}(\frac{\cos \mathrm{\&beta;}}{\cos \mathrm{\&alpha;}\sqrt{{(1/\mathrm{\&lambda;})}^2-{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2006100843262E00011.png,H2006100843262E00051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}}}+1)$

As seen still as the situation of disregarding ovality, turning right, ° speed of locating is identical in β+180 with left rotor for the speed of son at the β place.Figure 31～37 are for considering ovality and the comparison of disregarding left and right piston speed under the ovality situation, the speed of left rotor when ovality is disregarded in 1 expression among the figure, the speed of right-hand rotation when ovality is disregarded in 1 ' expression, the speed of left rotor when ovality is considered in 2 expressions, the speed of the son of turning right when ovality is considered in 2 ' expression.As can be seen from the figure, at λ (and/or α) hour, α can cause two kinds of velocity contrasts under the situation hardly, and only α just can cause some difference when λ is big.As seen do not consider that ovality can't cause too mistake, unless pressure is had accurate requirement.

If rotor is that line contacts with piston, no matter then can prove whether consider ovality, the motion of two rotors (piston) is simple harmonic motion all, is symmetrical fully, and equipment intracavity space length is constant.

3, eliminate that two-piston inner face spacing changes measure---the piston outer end contacts with the rotor tangent line

If in some cases equipment operating space length is remained unchanged, it is δ=0, that is keep distance between the two-piston inner face in mechanism's running, to equal among Fig. 1 equipment all the time from the length between o-o to o '-o ' cross section, can install a contact 12 in the piston outer end, contact is contacted with rotor.So just can make the motion of left and right sides rotor and piston is simple harmonic motion all, thereby makes the motion of two rotors symmetrical fully, i.e. δ=0.Now prove as follows.Consult Figure 38 to 40.

Left rotor: kb=ecos β z ₁=R+ecos β

Contact wire to the distance of equilbrium position 0-0 is

z＝z ₁-R＝ecosβ (17)

It is sub to turn right: kb=ecos β z ₂=R-ecos β

Contact wire to the distance of equilbrium position 0-0 is

-z′＝R-z ₂＝ecosβ

z′＝-ecosβ (18)

As seen when the piston outer end contacted with the rotor tangent line, the motion of left and right rotor was simple harmonic motion all, was symmetrical fully, and the length between two-piston is with invariable.

When 4 rotors contacted with the outer end points of piston, the motion of left and right piston is the reason of symmetry not exclusively

Prove that below when the outer end points of rotor and piston contact, left and right piston was separately with the operation of simple harmonic oscillation rule, displacement of the two and incomplete symmetry, promptly left piston descend (rising) distance and be not equal to the distance of right piston rising (decline).Why this thing happens because geometric error causes.Referring to Figure 41, when rotor contacted with the outer end points of piston, the residing height in left piston outer end was e-e, and rotor is when contacting with the piston line, the residing height in left piston outer end is f-f, and f-f is the tangent line at rotor cross-section peak place, contacts with rotor as contact.The difference of releasing e-e and f-f position easily by geometrical analysis just

In like manner, when rotor contacted with piston point, the residing height in right piston outer end was d-d, and rotor is when contacting with the piston tangent line, and the residing height in right piston outer end is c-c, and c-c is the tangent line at rotor cross-section peak place, contacts with rotor as contact.The difference of releasing c-c and d-d position easily by geometrical analysis also just

Obvious by Figure 41, Δ/2nd, under the left piston point contact situation than the distance that descends from peak under the tangent line contact situation more, also be under the right piston point contact situation than lacking the distance that rises from minimum point under the tangent line contact situation, sum of the two is the value added of device space length just If left and right piston outer end all arrives the tangent position at rotor cross-section peak place in the rotor operation process, promptly as the situation of tangent line contact, then left and right piston must move with simple harmonic oscillation, thereby keeps the distance between the two-piston inner face constant.Figure 42 further illustrates the difference that a contact contacts with tangent line, and dotted line is a tangent line contact situation among the figure.

Claims (6)

1. rotor mechanical device, comprise piston (10), piston waveguide tube (4), equipment (6) and rotor (3), piston (10) becomes to seal with piston waveguide tube (4) can be movingly, rotor (3) driven plunger (10) is moved in piston waveguide tube (4), it is characterized in that: piston (10) comprises left piston and right piston, on a left side, right piston outer end is provided with respectively and a left side, the vertical contact (12) of center line of right piston, contact (12) contacts with rotor (3) and makes in rotor (3) motion process a left side, right piston outer end all arrives the tangent position of rotor (3) cross section peak, the reciprocating motion of piston this moment (10) is simple harmonic oscillation, equipment (6) is on a left side, locus between the right two-piston inner face changes by the simple harmonic oscillation rule, and the space size remains unchanged.

2. rotor mechanical device according to claim 1, it is characterized in that: described rotor (3) comprises disc-like rotor or column rotor, rotor (3) is fixed or removable in its rotor shaft direction, and the geometrical axis of rotor (3) intersects or intersects with its rotating shaft (2) or be parallel or overlap.

3. rotor mechanical device according to claim 2 is characterized in that: described disc-like rotor (3) comprises circular section rotor or on-circular cross-section rotor, and described column rotor (3) comprises cylinder, round platform or on-circular cross-section cylinder.

4. rotor mechanical device according to claim 3 is characterized in that: to on-circular cross-section rotor (3), the variable in distance between stroke, speed and two-piston (10) inner face of piston (10) can determine by the concrete cross sectional shape of design rotor (3).

5. rotor mechanical device according to claim 1 is characterized in that: the geometrical axis of described piston (10) intersects or intersects with the geometrical axis or the rotating shaft (2) of rotor (3).

6. rotor mechanical device according to claim 1 is characterized in that: the shape of described equipment (6) comprises curve-like or linearity, and mounting means is vertical horizontal or tilting.

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